As I have been preparing for the new academic year over the past summer, I have been discovering the concepts of growth mindset and maths mindset mainly through the book “Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching” by Jo Boaler from Stanford. It is an amazing read and I cannot recommend it highly enough!
Discovering this has nudged me into thinking about how the teaching system for Cambridge maths works. Most of us tell new first years, and any students at open days, that they will do most of their learning through doing example sheets (that is, doing problems on lecture material) and getting stuck and trying again. This fits exactly into the growth mindset. In fact, the Cambridge supervision system is very supportive of this mindset: as example sheets are not graded at all, and are discussed in very personal supervisions (two students, one supervisor), students have the freedom to try challenging questions and to stretch themselves instead of going for the questions they already know they can do to get necessary marks. The whole teaching year from October to May can be used to explore harder questions and to stretch oneself.
I love one of the sentences in the book mentioned above, given by Carol Dweck who pioneered the growth mindset: “Every time you make a mistake, your brain grows a new synapse.” Isn’t that amazing? And through not penalising our students when they try hard questions on example sheets, we give them the environment to do exactly that: to grow their brains by working on problem, making mistakes, getting stuck, keeping going, and so on.
When I studied for one year in Germany, the first year of the maths degree there, our homework was graded and you needed a certain percentage over the whole semester to be admitted to write the exam at the end to pass that particular course. Of course this meant I, and in fact most of us, picked the easier questions where we knew we’d get the points. Or indeed some of my friends would just copy my answers… This kind of behaviour is not conducive to learning, and it does not give the students here at Cambridge any advantages. Of course I can’t say that none of them do it, I expect some of that goes on as well, but that is because they perhaps have not understood the advantages of the freedom of our system to be allowed to make mistakes while you learn without any penalties.
So, I urge all new (and indeed continuing) maths undergraduates: take full advantage of stretching yourself with complex and challenging questions! Do not be afraid to hand in partial solutions, or to say exactly which bit you did not understand, or got stuck on! Make good use of your supervisions (which are one of the most important and most special aspects of a Cambridge University education) by asking your supervisor questions about what you have not understood or what you want especially to discuss.
Let us all make our brains grow this academic year!